228 



of more than 6" in temperature, and about 20 inches of mercury in 

 the pressure of the vapour. 



The author entered into a comparison of the empirical formulae 

 which have been successively employed to express in mathemati- 

 cal terms the simultaneous progressions of temperature and elas- 

 tic force. These are of two classes : the first comprehends the 

 formulae of Prony, Laplace, Biot, and Ivory, in which the elasticity 

 is the sum of the terms of an infinite series, of which five terms at 

 least now require to be taken ; and it was shewn that, even with 

 an operation so tedious and laborious, the results of calculation 

 differ from those of experiment still more widely even than those 

 from each other. The formulae are as follows : — 



(1.) F^=^.< + /*,e* + -"»e|, &c Prouy. 



(2.) Ft = Log 160 + at + r=t'^+ yt^ + &c. . . Laplace. 



(3.) F, = 0^.76.10 A* + Bt« + C«3 + &c. , giot. 



(4.) F = 0.0087466 4 — 0.000015178 t'^ + 00000002483 1^ + Ivory. 



30 



The other class of formulae are those of Dr Young and his fol- 

 lowers. He was the first to give a manageable expression of a 

 simple form, in which the expression for the elastic force of the 

 vapour is merely a multiple of the temperature, increased by a 

 constant quantity, and placed under the index 7. This simpler 

 expression, although absolutely empirical, having been selected by 

 Dr Young, as he candidly avows, from above a dozen others, mere- 

 ly because it happened to approximate to the best experiments he 

 at that time possessed, yet has been almost invariably followed ever 

 since. But while the form of the expression has been preserved, 

 it has been found necessary to alter the value of its terms at each 

 step of experimental research, in such a manner that this branch of 

 knowledge now appears to have become degraded to the very 

 lowest degree of empiricism. Dr Young's expression having been 

 found too high for the subsequent experiments of Southern, the 

 index was reduced from 7. to 5.13. Dr Ure's experiments next 

 made their appearance, and forthwith the index 7 being found too 

 great, and 5.13 too small, the number 6. was adopted as best re- 

 presenting them. The subject being next examined by M. Coriolis, 

 who, reviewing the works of all his predecessors, found none of 

 them sufficiently consistent, he satisfied himself with taking an 

 average of the whole, and obtaining as an index the mean number 



